Run-to-run control utilizing virtual metrology in semiconductor manufacturing

ABSTRACT

An apparatus for performing run-to-run control and sampling optimization in a semiconductor manufacturing process includes at least one control module. The control module is operative: to determine a process output and corresponding metrology error associated with an actual metrology for a current processing run in the semiconductor manufacturing process; to determine a predicted process output and corresponding prediction error associated with a virtual metrology for the current processing run; and to control at least one parameter corresponding to a subsequent processing run as a function of the metrology error and the prediction error.

CROSS-REFERENCE TO RELATED APPLICATION(S)

The present application is a continuation of U.S. patent applicationSer. No. 13/557,955, filed Jul. 25, 2012, the entire contents of whichare expressly incorporated herein by reference in its entirety for allpurposes.

FIELD OF THE INVENTION

The present invention relates generally to the electrical, electronic,and computer arts, and more particularly relates to semiconductormanufacturing.

BACKGROUND

Virtual metrology (VM) generally refers to a model-based prediction ofsome process outcome in place of, or in the absence of, an actualphysical measurement of that outcome. The underlying models are learnedfrom histories of the actual physical outcomes and predictors that mayinclude process trace data, tool consumable status, and incoming workcharacteristics, among other factors. If the models are sufficientlyaccurate predictors of process outcomes, VM applications present anopportunity to reduce the number of physical measurements made tomonitor a given process, while maintaining or even improving qualitycontrol. Such applications are especially attractive for highly complex,capital-intensive semiconductor manufacturing lines in whichmeasurements monitoring processes may add significant processing timeand cost.

SUMMARY

Embodiments of the invention provide methods and apparatus for improvingrun-to-run (R2R) control in a semiconductor manufacturing process in amanner which is beneficially adapted to account for process drift. TheR2R control methodology according to aspects of the invention is basedon processing time which can avoid dealing with high dimensional processvariables, which typically have intricate dependencies among oneanother, and effectively reduce the process variation. The R2R controltechniques according to embodiments of the invention further provide ameans for optimizing semiconductor wafer inspection policy.

In accordance with an embodiment of the invention, a method forrun-to-run control and sampling optimization in a semiconductormanufacturing process includes the steps of: determining a processoutput and corresponding metrology error associated with an actualmetrology for a current processing run in the semiconductormanufacturing process; determining a predicted process output andcorresponding prediction error associated with a virtual metrology forthe current processing run; and controlling at least one parametercorresponding to a subsequent processing run as a function of themetrology error and the prediction error.

As used herein, “facilitating” an action includes performing the action,making the action easier, helping to carry the action out, or causingthe action to be performed. Thus, by way of example and not limitation,instructions executing on one processor might facilitate an actioncarried out by instructions executing on a remote processor, by sendingappropriate data or commands to cause or aid the action to be performed.For the avoidance of doubt, where an actor facilitates an action byother than performing the action, the action is nevertheless performedby some entity or combination of entities.

One or more embodiments of the invention or elements thereof can beimplemented in the form of a computer program product including acomputer readable storage medium with computer usable program code forperforming the method steps indicated. Furthermore, one or moreembodiments of the invention or elements thereof can be implemented inthe form of a system (or apparatus) including a memory, and at least oneprocessor that is coupled to the memory and operative to performexemplary method steps. Yet further, in another aspect, one or moreembodiments of the invention or elements thereof can be implemented inthe form of means for carrying out one or more of the method stepsdescribed herein; the means can include (i) hardware module(s), (ii)software module(s) stored in a computer readable storage medium (ormultiple such media) and implemented on a hardware processor, or (iii) acombination of (i) and (ii); any of (i)-(iii) implement the specifictechniques set forth herein.

These and other features and advantages of the present invention willbecome apparent from the following detailed description of illustrativeembodiments thereof, which is to be read in connection with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The following drawings are presented by way of example only and withoutlimitation, wherein like reference numerals (when used) indicatecorresponding elements throughout the several views, and wherein:

FIG. 1 is a block diagram conceptually depicting a method of samplingfor metrology to monitor process performance during semiconductormanufacturing;

FIG. 2 conceptually depicts the conversion of tensors (embodying rawdata) into one-dimensional vectors;

FIG. 3 graphically depicts a comparison of root mean square error (RMSE)versus chamber identifier (ID) for five different prediction models;

FIG. 4 is a block diagram depicting at least a portion of an exemplarysystem for R2R control and sampling optimization, according to anembodiment of the invention;

FIG. 5 is a flow diagram depicting at least a portion of an exemplarymethodology for implementing the illustrative R2R control system shownin FIG. 4, according to embodiment of the invention;

FIG. 6 is a flow diagram depicting at least a portion of an exemplaryR2R control methodology, according to embodiment of the invention;

FIG. 7 is a flow diagram depicting at least a portion of an exemplarysampling policy optimization methodology, according to an embodiment ofthe invention; and

FIG. 8 is a flow diagram conceptually depicting at least a portion of anexemplary methodology for generating a metrology-based prediction model,according to an embodiment of the invention.

It is to be appreciated that elements in the figures are illustrated forsimplicity and clarity. Common but well-understood elements that may beuseful or necessary in a commercially feasible embodiment may not beshown in order to facilitate a less hindered view of the illustratedembodiments.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Aspects of the present invention will be described herein in the contextof illustrative methods and apparatus for enhancing run-to-run (R2R)control using virtual metrology (VM) to reduce process variation insemiconductor manufacturing. It is to be appreciated, however, that theinvention is not limited to the specific apparatus and/or methodsillustratively shown and described herein. Moreover, it will becomeapparent to those skilled in the art given the teachings herein thatnumerous modifications can be made to the embodiments shown that arewithin the scope of the present invention. That is, no limitations withrespect to the specific embodiments described herein are intended orshould be inferred.

In semiconductor manufacturing, wafers go through hundreds of processesto finally yield integrated circuit devices. Each process generallyfollows a given recipe that defines detailed fabrication steps andsettings of the process variables. FIG. 1 is a high-level block diagramwhich conceptually depicts sampling for metrology to monitor processperformance during semiconductor manufacturing. As shown in FIG. 1,since the manufacturing process is quite complex, wafers in selectedlots (e.g., lots k and k+1, where k is an integer) are sampled formetrology to monitor the process performance. Based on the metrologyresults, the process control system will take appropriate action toadjust one or more process parameters (e.g., exposure time, depositionrate, oxide growth rate, temperature, doping concentration, etc.) by lotor by wafer. However, this standard metrology and control scheme isbased on an assumption that there is no abrupt process drift betweenmeasured wafers, which is often not the case. Moreover, due to metrologydelay (e.g., up to three days for plasma etch process), there can be alarge time gap for process control. To fill this information gap betweenmeasured wafers and the time gap in process control, timelywafer-by-wafer metrology is indispensable.

Modern semiconductor processing tools publish large amounts of real-timedata which can, to some extent, reflect the actual processingconditions. Therefore, in recent years VM, which involves buildingmodels to predict wafer quality based on historical measurements and thecorresponding process variables, has received a lot of attention in thesemiconductor industry. The predicted wafer quality can then facilitatetimely process control, detect faulty wafers early in the process, andimprove productivity by reducing actual metrology frequency (i.e.,sampling frequency).

For this purpose, statistical models based on one-dimensional vectorshave been constructed, such as, for example, multiple regression withfeature selection, partial least squares, support vector regression(SVR), and artificial neural networks. However, process data insemiconductor manufacturing usually come in the form of tensors, ormultidimensional arrays. For example, in plasma deposition operations,each recipe process usually has multiple steps. During each step,process variables, such as, but not limited to, temperature, pressureand gas flow per unit time can be observed. Therefore, to predict thewafer quality, the input data are naturally expressed as third-ordertensors—the three dimensions or modes being steps, time (e.g., seconds)within a step, and observed process variables, or features—orsecond-order tensors, if summary statistics are used for each processvariable in a single step instead of instantaneous measurements.

FIG. 2 conceptually depicts conversion of tensors (embodying raw data)into one-dimensional vectors. As a result of the process of convertingtensors into vectors, however, significant information embedded in thestructure of the tensors can be lost, such as, for instance, featurecorrespondence in different steps. Consequently, a prediction modelwhich utilizes tensor inputs, rather than vectorized inputs, ispreferred.

Since VM serves to predict every wafer's metrology values, it enables,among other things, R2R control at the wafer level (i.e., wafer-to-wafercontrol). Compared to a traditional lot-to-lot control scheme,wafer-to-wafer control schemes based on a combination of virtual andactual metrology values can potentially achieve a number of importantbenefits, such as, but not limited to, enhanced final yield, predictiveequipment maintenance, and improved productivity. For this object,exponentially weighted moving average (EWMA) controllers and itsvariations are widely used to adjust the recipe parameters in existingwork. However, for processes with severe drifts, an EWMA controller isinsufficient even when large weights are used. This problem becomes moresevere when there is a metrology delay, which is almost inevitable insemiconductor manufacturing. In addition, a typical recipe process canhave hundreds of variables with intricate dependencies among each other.These issues present challenges for R2R control utilizing VM.

In accordance with embodiments of the invention, several VM embedded R2Rcontrol schemes are provided that are operative to facilitate feedbackcontrol based on combining actual and virtual metrology values. The R2Rcontrollers are based on processing time, which can avoid dealing withhigh-dimensional process variables. An ability of the control schemesaccording to embodiments of the invention to effectively reduce processvariation is demonstrated herein below based on experiment results.Embodiments of the invention preferably utilize a wafer qualityprediction model for metrology variable prediction with tensor inputprocess variables by directly operating on the tensor. Experimentalresults demonstrate improved performance of this model compared tostandard approaches that deal with only one-dimensional inputs. Adetailed discussion of tensor-based wafer quality prediction models thatare suitable for use with embodiments of the invention are described inco-pending U.S. patent application Ser. No. 13/526,152 filed on Jun. 18,2012, the disclosure of which is expressly incorporated by referenceherein in its entirety for all purposes.

R2R control is a process control framework that adjusts process inputson a run-by-run basis as a function of information obtained duringand/or after the process, or prescribed stages of the process, havecompleted in order to improve productivity. The EWMA statistics and itsvariations are widely used as R2R controllers. In order to compromisethe impact of process drift, a double EWMA (dEWMA) controller, modifiedEWMA, predictor-corrector controller and a Bayesian enhanced EWMAcontroller are developed, according to embodiments of the invention.These controllers are operative to adjust one or more recipe settingsassociated with the process so the process, or parameters thereof, canbe brought to within prescribed target specifications. However, a recipeprocess may have hundreds of process variables, with at least a subsetof the variables having complex interrelationships. It has been shownthat one of the most effective manipulated variables in R2R control isprocessing time, such as, for example, etch time, exposure time and/orplanarization time. (See, e.g., S. J. Qin, et al., “Semiconductormanufacturing process control and monitoring: A fab-wide framework,”Journal of Process Control, 16(3): 179-191, 2006, the disclosure ofwhich is incorporated herein by reference in its entirety.)

Suppose the process output can be described asy _(n) = r _(n) t _(n),  (1)where t_(n) and r _(n) represent processing time and average processingrate, respectively, for a given run n. Based on this relationship, threeVM embedded control schemes are presented, according to embodiments ofthe invention, although it is to be understood that the invention is notlimited to the control schemes described herein. These control schemesare not only able to quickly adapt to process drifts, but they also leadto larger reduction in process variation compared to what can beachieved by actual metrology alone.

As will be described in further detail below, a tensor-based model forwafer quality prediction is constructed which can incorporate priorknowledge from various sources in a principled way. First, certainnotation used throughout the description will be presented; then, anobjective function will be described; and finally, performance of themodel on real production data sets will be demonstrated.

Assume there are N training examples {χ_(n),y_(n)}, n=1, . . . , N,where χ_(n) ε

^(d) ¹ ^(×d) ² ^(× . . . ×d) ^(K) is a K-dimensional array, orK^(th)-order tensor, and y_(n) ε

is the response variable. Notice that for χ_(n), K is the dimension ofthis array of the number of modes of this tensor, and d_(K) is thenumber of elements along the k^(th) dimension, k=1, . . . , K.Therefore, the total number of input features is Π_(k=1) ^(K)d_(k). WhenK=1, the input χ_(n) is a vector, and the problem is reduced to regularregression; when K=2, χ_(n) is a matrix; when K>2, χ_(n) is aK^(th)-order tensor. For the present discussion, we focus on cases whereK>1.

Let

,

ε

^(d) ¹ ^(×d) ² ^(× . . . ×d) ^(K) denote two tensors. Define

,

to be the inner products of their corresponding elements. Furthermore,define the norm of tensor ∥

∥=

. The value of y_(n) is predicted using a linear model, thus we have aweight tensor

ε

^(d) ¹ ^(×d) ² ^(× . . . ×d) ^(K) , which is the same size as χ_(n). Wefirst approximate the weight tensor using a rank-one tensor whoseCandecomp/Parafac (CP) decomposition is, in turn, approximated based onprior information.

More particularly, we minimize a loss function L(y_(n),

χ_(n),

) summed over all training examples. Here, we require that L(•,•) is thesquared loss and convex with respect to the second argument. Based onthe tensor structure, it is assumed that the weight tensor

can be approximated by a rank-one tensor with CP decomposition α₁ ^(o)α₂^(o) . . . ^(o)α_(K), where α_(k) ε

^(d) ^(k) is the weight vector for the k^(th) mode. α_(k) reflects thegeneral importance of the k^(th) mode of the input tensors. In otherwords, ∥

−α₁ ^(o)α₂ ^(o) . . . ^(o)α_(K)∥² should be small. Intuitively, α_(k)measures the contribution of the k^(th) mode of χ_(n) to the outputy_(n).

For example, when K=2,

is a matrix, and

(i, j) should be close to α₁(i)×α₂(j), where

(i, j) is the element of

in the i^(th) row and j^(th) column, α₁(i) is the i^(th) element of α₁,and α₂(j) is the j^(th) element of α₂. Furthermore, for each α_(k), itis assumed that it is close to vector α_(k) ε

^(d) ^(k) , which is known a priori and reflects the domain knowledge.Putting everything together, the following objective function isobtained:minƒ(

,α₁, . . . ,α_(K))=Σ_(n=1) ^(N) L(y _(n),

χ_(n),

)+γ₀∥

−α₁ ^(o)α₂ ^(o) . . . ^(o)α_(K)∥²+Σ_(k=1) ^(K)γ_(k)∥α_(k)−α_(k0)∥²,  (2)where γ₀, γ₁, . . . , γ_(K) are positive parameters that balance amongdifferent terms. In particular, the relative values of γ₀, . . . , γ_(K)reflect a confidence in using prior knowledge to approximate the weightvector in each mode: the bigger the value, the more confidence there isin this approximation. The weight tensor

in the objective function can be calculated using a block coordinatedecent (BCD), which is guaranteed to converge to a local optimum sincethe objection function has a unique minimum in each coordinate block.

A global model across one or more chambers can be expressed as:

$\begin{matrix}{{{\min\mspace{14mu}{f( {\beta_{1},{K\;\beta_{T}}} )}} = {{\sum\limits_{c = 1}^{T}\;{{Y_{c} - {X_{c}\beta_{c}}}}^{2}} + {\lambda_{1}{{\beta_{c} - \beta_{0}}}^{2}}}},} & (3)\end{matrix}$where Y_(c)εi^(n) denotes the quality of wafers from chamber c, andX_(c)εi^(n) ^(c) ^(×d) denotes the input process variables of chamber c.β_(c)εi^(d) are coefficient vectors and λ₁ is a positive parameter thatencourages all the β_(c) to be closed to the common vector β₀εi^(d). β₀reflects the chamber matching.

In accordance with an embodiment of the invention, exemplary steps forgenerating the global model include: approximating coefficientscorresponding to different chambers to a common vector given by priorinformation on tool capability matching; adding a positive coefficientto balance different terms (i.e., adding regularization to prevent modelover-fit); and minimizing the prediction error and optimizing theapproximation, for example using a block coordinate based algorithm.

A metrology-based prediction model can be expressed as:ŷ _(i) =y _(j),  (4)where j is the wafer index of the last measured wafer prior to time i.The value of ŷ_(i) can then be used as a component of a more generalpredictor. This component will be included with a weight w_(i) that isdetermined byw _(i) =γP(i−j),  (4A)where γ is a positive coefficient and P is the function that determinesan inverse of the variance of the predictor based on ŷ_(i) as a functionof i−j; i.e., the number of wafers since the last measured wafer.

A metrology and error-adaptive prediction model can be expressed as:y _(i)=γ(ε)y _(j)+β^(T) X _(i),  (5)where ŷ_(i) is defined as above, y_(j) is the quality of the lastmeasured wafer, X_(i) is the input process variable, and β^(T) denotes avector of coefficients. The quantity γ(ε) is a function of the metrologyor prediction bias or variation. A special case of this model isŷ _(i) =γy _(j)+β^(T) X _(i),  (6)Experimental Results: Case Study

By way of illustration only, a case study is presented in which theperformance of the prediction model is compared with those modelsutilizing vectorized inputs. Data is collected from an exemplary plasmadeposition process. A key measure of wafer quality is the depositionthickness. Each complete deposition process is comprised of multiplesteps. Processing conditions (e.g., gas flows, temperatures, plasmaproperties, etc.) and step durations vary significantly from step tostep. Process variables, such as, for example, gases and power, can takeon different values at different steps. Thus, the data can berepresented as a third-order tensor. In this study, summary statisticsof median for each variable are used. The first exemplary processincludes a total of 12 process variables. There are a total of 488target measurements and associated process variables collected for theprocess. The process variables and the outputs are normalized to havemean zero and standard deviation one. This process is run on 8 differentchambers, each with its own capability. The performance of fivedifferent exemplary models is compared. The five illustrative modelsare:

-   -   i. RR (ridge regression) model for dealing with vectorized        inputs, which has been widely used as a baseline prediction        model in VM applications for its simplicity and        interpretability;    -   ii. SVR model with radical basis function (RBF) kernel for        dealing with vectorized inputs;    -   iii. PLS (partial least square) regression model, which has been        widely used in chemical and process industry;    -   iv. H-MOTE model—Equation (2), with α_(k0) given by the domain        expert;    -   v. GM (global model)—Equation (3) with β₀ given by the domain        expert.

For all of the above models, parameters are chosen based oncross-validation in the training set only, and the cross-validationresults of Root Mean Squared Error (RMSE) are used for comparison, asshown in FIG. 3. In this figure, the x-axis indicates the chamber ID,and the y-axis indicates average RMSE. For the given data set, werandomly choose 80% for training and the remaining 20% as the test set.The experiments were run 50 times, and both the mean and the variancewere reported. As apparent from FIG. 3, the PLS model exhibits thehighest RMSE, varying between about 0.6 and about 0.95 across allchambers; the GM model exhibits the lowest RMSE, varying between about0.2 and about 0.3. The RR model exhibits slightly smaller RMSE than thePLS regression model. The SVR model is better than the RR and PLSregression models. The tensor-based method H-MOTE is better than the RR,PLS regression and SVR models, but worse than the global model GM interms of the RMSE.

From FIG. 3, at least two observations can be made. First, theperformance of H-MOTE is consistently better than PLS, RR and SVRmodels, which both take vectorized inputs. Second, the performance of GMoutperforms the single chamber based model.

According to embodiments of the invention, three exemplary R2R controlschemes are introduced based on processing time and their performance isevaluated based on three deposition processes. It is to be understood,however, that the invention is not limited to the exemplary R2R controlschemes described herein, but that other R2R control schemes within thescope of the present invention are contemplated, as will become apparentto those skilled in the art given the teachings herein. Utilizing VM,the control system can obtain metrology values for each wafer, measuredor not. Based on equation (1) above, the actual or virtual averageprocessing rates can be estimated. This information can then be used ina given run n to control the process time in a subsequent run n+1. Inthe first R2R control scheme,

t n + 1 = T ( 3 )where T is the process target (e.g., deposition thickness) and{circumflex over (r)} _(n) is the predicted average process rate of runn based on equation (2). When the actual metrology value is available inrun n, r _(n) is used instead. The process time t_(n+1) for run n+1 isused in the next run of production. An effectiveness of the schemevaries with the accuracy of the rate prediction which is, in turn, basedon the process variables and the VM model.

In the second R2R control scheme,

$\begin{matrix}{{t_{n + 1} = \frac{T}{{\alpha\;{\overset{\_}{r}}_{n,{- 1}}} + {( {1 - \alpha} )}}},{0 \leq \alpha \leq 1}} & (4)\end{matrix}$where r _(n,−1) is the average rate calculated based on the last actualmetrology value, and α is a weight that can be chosen according to theVM error. Thus, when α=1, the control scheme proposes the nextprocessing time based on the last measurement alone. The performance ofthe control scheme depends on a strength of the process autocorrelation,and the frequency and availability of actual metrology. When α=0, thecontrol scheme reduces to the first R2R control scheme previouslydiscussed. According to aspects of the invention, the R2R controller isoperative to dynamically adjust the respective weights given to theactual metrology value and the virtual metrology value in a manner whichoptimizes a sampling policy of the process (e.g., sampling frequency).

In the third R2R control scheme,

$\begin{matrix}{t_{n + 1} = \frac{T}{{{\alpha(ɛ)}{\overset{\_}{r}}_{n,{- 1}}} + {\lbrack {1 - {\alpha(ɛ)}} \rbrack}}} & (5)\end{matrix}$where ε represents a number of factors related to prediction errors. Theweight α(•) can take on various forms, but its value must be constrainedin the range [0, 1]. For example, we can use a quadratic function

${\alpha(ɛ)} = \lbrack \frac{ɛ_{- 1}^{T}}{\max( {ɛ_{- m}^{T}} )} \rbrack^{2}$in equation (5) above, where ε⁻¹ ^(T) is the prediction errorcorresponding to the last actual metrology and max(|ε_(−m) ^(T)|) is themaximum absolute prediction error among the last m wafers. When theprediction error is small, this control scheme favors the VM prediction.Other forms of α(•) can also be incorporated that depend on variances ofdifferent predictors obtained in parallel. The third R2R control schemecan thus increase the smoothness of time adjustment, balance the impactof VM error compared to the first and second R2R control schemes, andadjust the weight automatically.

In Table 1 below, each of the three illustrative R2R control schemesaccording to embodiments of the invention are compared with one anotherin terms of standard deviations of the wafer thickness that thoseprocesses experimentally produce; the biases of these control schemeswere negligible. Assume α=0.2 in the second control scheme, Table 1indicates that the standard deviation of the thicknesses for the thirdcontrol scheme is the smallest compared to that for the other two cases.For all three processes, the standard deviations of the thicknessesobtained under R2R control are smaller than those without R2R control,thus demonstrating the superiority of the methods according toembodiments of the invention. More particularly, the case “without R2Rcontrol” represents a standard feedback control practice that isrestricted to the availability of actual metrology values and conductedfrom lot to lot. This suggests the possibility for measurement ratereduction, given the current tolerance for process variation. In Table1, the mean absolute prediction error is also shown, which influencesthe R2R control in VM applications.

TABLE 1 σ Process 1 Process 2 Process 3 Without R2R Control 64.16 79.9588.15 First Control Scheme 58.04 66.11 68.98 (−10%) (−17%) (−22%) SecondControl Scheme 56.81 62.66 64.43 (−11%) (−22%) (−27%) Third ControlScheme 57.81 64.89 63.59 (−12%) (−19%) (−28%)$\frac{\sum\;{{y_{i} - {\hat{y}}_{i}}}}{n}$ 34.16 (T = 6250) 38.32 (T= 6250) 37.73 (T = 6250)

As will be appreciated by one skilled in the art, aspects of the presentinvention may be embodied as a system, method or computer programproduct. Accordingly, aspects of the present invention may take the formof an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, aspects of the present invention may take the form of acomputer program product, the computer program product in turncomprising a tangible computer readable storage medium storing in anon-transitory manner executable program instructions which, whenexecuted, implement method steps according to an embodiment of theinvention.

By way of illustration only, FIG. 4 is a block diagram depicting atleast a portion of an exemplary system 400 for performing R2R controland sampling optimization, according to an embodiment of the invention.The R2R control system 400 includes a data storage unit 402, oralternative memory (e.g., embedded and/or standalone), a metrologymodule 404, a sampling optimization module 406, a predictive modelingmodule 408, and a control module 410. The R2R control system 400receives prescribed information, including but not limited to actualmetrology measurements, from manufacturing tools 412, which includes,for example, semiconductor processing equipment, metrology equipment,automated test equipment (ATE), etc.

Data storage unit 402 is operative to at least temporarily store certaininformation which may be used by the system 400, such as, for example,the results of actual measurements performed by the manufacturing tools412 (e.g., wafer inspection), processing variables, etc., which may beused by one or more other modules in the system. The data storage unit402 can be implemented, for example, as a database or alternativememory.

Metrology module 404 is essentially a device or apparatus operative toreceive, from the manufacturing tools 412, one or more actual measuredwafer parameters (e.g., oxide/film thickness, geometry, strength, etc.)and to generate an output that is indicative of actual measured waferquality. For example, in one embodiment, metrology module 404 isoperative to compare a measured process parameter (e.g., thickness of adeposited film) with a prescribed target value for that parameter (e.g.,desired film thickness) and, based on how close the measured parameteris to the target value, generate the output indicative of wafer quality.

The predictive modeling module 408 is operative to receive prescribedinformation from the manufacturing tools 412, such as, for example,parameters indicating chamber capacity matching information, etc., andto generate therefrom a prediction model which, in one embodiment, isindicative of predicted wafer quality. Any one or more of the virtualmetrology models discussed above are suitable for use with thepredictive modeling module 408. The predictive modeling module 408 isoperative to generate an output that is indicative of predicted waferquality.

The sampling and optimization module 406 is operative to receive, amongother parameters, the output indicative of actual measured wafer qualitygenerated by the metrology module 404 and the output indicative ofpredicted wafer quality generated by the predictive modeling module 408,and is operative to generate an output adapted to optimize a samplingpolicy of the system 400. In one embodiment, optimizing the samplingpolicy comprises minimizing a sampling frequency of the system 400,although the invention is not limited to minimizing the samplingfrequency. The sampling policy information generated by the sampling andoptimization module 406 can be passed to the metrology module 404 forcontrolling the measurement of wafer parameters. A determination as towhether or not to measure individual wafers may also be generated by thesampling and optimization module 406 and provided to the metrologymodule 404.

The sampling and optimization module 406 is further operative to passcertain information to the predictive modeling module for controllingthe model(s) upon which the wafer quality prediction is based to update(i.e., refresh) the model(s) and improve an accuracy thereof. In thisregard, the sampling and optimization module 406 is operative todetermine when a confidence in the virtual metrology (i.e., predictivemodel) has fallen below some prescribed target value so as to requiretaking actual metrology measurements to correct the predictive model. Asan accuracy of the predictive model increases, a sampling frequencypreferably decreases. A function of the sampling and optimization module406 is therefore to minimize the sampling frequency.

By way of example only, consider a scenario in which the growth rate ofoxide is monitored. While perhaps the most accurate approach may be totake actual measurements of oxide thickness on the wafers, such anapproach is prohibitively costly and time consuming. A faster and lesscostly approach would be to rely on virtual metrology predictionresults, but such results may not yield a desired level of accuracy. Thesampling and optimization module 406, in this illustrative scenario, isoperative to control a balance between a reliance on virtual metrology,comprising predictive modeling, and actual metrology to achieve adesired level of accuracy using a minimum sampling frequency (i.e.,taking a minimal number of actual measurements).

The control module 410 is coupled with the manufacturing tools 412 andthe sampling optimization module 406 in a feedback arrangement forcontrolling certain aspects of the manufacturing tools (e.g., processingparameters) for R2R control. More particularly, the control module 410is operative to receive the sampling policy generated by the samplingand optimization module 406 and to control the manufacturing tools 412in accordance with the sampling policy.

FIG. 5 is a flow diagram depicting at least a portion of an exemplarymethodology 500 for implementing the R2R control system 400 shown inFIG. 4, according to embodiment of the invention. In the description ofmethod 500 below, the term “module” will be used to define a particularstep or function. Although illustrated as being comprised of a pluralityof functional modules for clarity purposes, it is to be appreciated thatone or more modules, or portions thereof, may be combined and/orincorporated into one or more other modules, in accordance with aspectsof the invention.

With reference to FIG. 5, in module 502, one or more metrology variablesfor VM and R2R control are identified. Metrology variables, which may beidentified by a user and/or manufacturing or alternative tools (eithermanually or automated), may include, but are not limited to, processoutput parameters, such as, for example, film/oxide thickness, geometry,etc. At least a subset of the metrology variables are preferablyprovided to module 504 which is operative to collect processingvariables associated with the received metrology variables. In module506, parameters indicative of chamber capacity matching are collectedfor further processing. At least a subset of the metrology variables(either the same or a different subset as that received by module 504)are also provided to module 508, which is operative to collect metrologydata associated with the received metrology variables. At least aportion of the metrology data is used by module 510 to estimate ametrology error and determine therefrom a deviation from prescribedtarget values.

The methodology 500 utilizes a plurality of prediction models 512, eachprediction model being operative to generate an output result as afunction of actual and/or virtual metrology data. In this illustrativeembodiment, prediction models 512 includes four prediction models;namely, a single chamber based model 514, a global model across all (ormultiple) chambers 516, a metrology based prediction model 518 and ametrology and error-adaptive model 520. The single chamber based model514 is operative to receive processing variables from module 504corresponding to one semiconductor processing chamber and construct aprediction model as a function thereof. The global model 516 isoperative to receive parameters indicative of chamber capacity matchingfrom module 506 and processing variables from module 504 correspondingto all, or at least a plurality, of the semiconductor processingchambers and to construct a prediction model as a function thereof. Themetrology based prediction model 518 is operative to receive actualmetrology measurement data from module 508 and variance curveinformation retrieved from a knowledge base or alternative storageelement (e.g., storage unit 402 in FIG. 4) to build a prediction modelbased on the actual metrology measurement data and variance curve. Themetrology and error-adaptive model 520 is operative to receiveprocessing information from metrology tools (e.g., manufacturing tools412 in FIG. 4) and metrology error and variation information from module510, and to build a prediction model as a function thereof. Each ofthese prediction models is described in further detail herein above. Forexample, the single chamber based model 514 and global model 516 areexpressed using equation (3) above; the metrology based prediction model518 is expressed using equation (4); and the metrology anderror-adaptive model 520 is expressed using equations (5) and (6).Results from one or more of the predictions models 514, 516, 518 and 520are used by a virtual metrology module 522 to generate a measurementprediction output therefrom and are used by a prediction error module524 to generate a prediction error output therefrom.

Method 500, in module 526, is operative to perform metrology toolmatching. Results from module 526 are provided to a sampling/measurementoptimization module 528. The sampling/measurement optimization module528 is preferably operative in a manner consistent with the sampling andoptimization module 406 shown in FIG. 4 and described above. Moreparticularly, sampling/measurement optimization module 528 is operativeto generate a sampling policy for controlling the collection ofmetrology data as a function of one or more of metrology tool matchingresults from module 526, measurement prediction results from virtualmetrology module 522 and prediction error results from prediction errormodule 524. Accordingly, the sampling policy output generated by thesampling/measurement optimization module 528 is provided to module 508to facilitate the collection of metrology data.

An R2R controller 530 is operative to receive measurement predictionresults from virtual metrology module 522, prediction error results fromprediction error module 524, and estimated metrology error and variationresults from module 510. The R2R controller 530 is preferably operativein a manner consistent with the control module 410 shown in FIG. 4 anddescribed above. Specifically, the R2R controller 530 is operative in afeedback control arrangement to control one or more manufacturing tools532 in accordance with the sampling policy generated by thesampling/measurement optimization module 528. The manufacturing tools532 are used to produce wafers and generate processing variables 534,which can be used by subsequent processing steps to adjust themanufacturing process to meet prescribed parameters.

FIG. 6 is a flow diagram depicting at least a portion of an exemplaryR2R control methodology 600, according to embodiment of the invention.The illustrative R2R control methodology 600 may be implemented, atleast in part, in the control module 410 shown in FIG. 4. With referenceto FIG. 6, in step 602, processing time of the i^(th) run, t_(i), isstored. This processing time is updated for subsequent runs. Theprocessing time, in this embodiment, is used as an identified controlparameter, although the invention is not limited to using processingtime as a control parameter. Moreover, more than one control parametermay be employed, according to other embodiments.

In step 604, actual metrology measurements, y_(j) and r_(j) (j≦i, i andj are integers), are obtained, where y_(i) is indicative of a processparameter (e.g., deposition thickness) which may be used as a waferquality metric, and r_(i) is indicative of a rate of processing (e.g.,deposition rate) corresponding to the i^(th) wafer. For example, inaccordance with equation (1) above, y_(i)= r _(i)t_(i), where y_(i) isdeposition thickness corresponding to the i^(th) wafer, r _(i) isaverage deposition rate, and t_(i) is deposition time. An outputmeasured wafer parameter generated in Step 604 is provided to a R2Rcontroller 616 whereby adjustments to the process can be performed asappropriate.

The actual measured wafer parameter is also used to determine metrologyerror in step 612 by comparing the actual measurement generated from themetrology in step 604 with an expected value for that wafer parameter. Adiscrepancy between the actual and expected results, taking in account astatistical accuracy of the metrology tools, is used to generate anoutput indicative of a confidence in the actual measurement. This outputis provided to the R2R controller 616. Based on the amount ofdiscrepancy between actual and expected results collected over time, anindication as to how to adjust the process variables.

In step 606, parameters indicating chamber capacity matching areobtained. These parameters represent factors relating to uncertainty andchamber capabilities. With regard to chamber capacity matching, athreshold is given for chamber capacity matching. If the difference of aparticular chamber's capacity relative to other chambers is greater thanthe given threshold, the chamber processing parameters are adjusted tomatch its capacity to the other chambers. These chamber matchingparameters are a subset of the parameters which may be used by the R2Rcontroller 616 in determining a time, t_(i+1), for the next processingrun. A chamber mismatch triggers control immediately.

In step 608, a target, T, of the process output is obtained. The target,which is indicative of a desired value of the process output parameter,is provided to the R2R controller 616 and is used to control theparameters such as time for the subsequent run.

In step 610, a virtual metrology prediction model is generated based onparameters ŷ_(i) and {circumflex over (r)}_(i), where ŷ_(i) isindicative of a predicted process parameter (e.g., deposition thickness)which may be used to output a prediction of i^(th) wafer quality wafer,and {circumflex over (r)}_(i) is indicative of a predicted rate of time(e.g., deposition rate) corresponding to the i^(th) wafer. The predictedwafer quality output is provided to the R2R controller 616 and is alsoused to determine a prediction error in step 614. This prediction erroroutput is provided to the R2R controller 616.

In accordance with principles of the invention, the R2R controller 616is operative to receive the output from step 612 indicative of metrologyerror associated with the actual metrology and the output from step 614indicative of prediction error associated with the virtual metrology,and to assign weights to the actual and virtual metrology results. Theweight assigned to each of the actual and virtual metrology parametersis indicative of a statistical confidence in the respective parameters;a sum of the weights is equal to one. For example, a weight of 1.0(100%) assigned to the actual metrology parameter and a weight of 0 (0%)assigned to the virtual metrology parameter indicates completeconfidence in the actual metrology measurement and no confidence in theprediction model. Likewise, a weight of 0.8 (80%) assigned to thevirtual metrology parameter and a weight of 0.2 (20%) assigned to theactual metrology parameter indicates a higher confidence in theprediction model compared with the actual metrology measurement;consequently, there is no need to take an actual measurement to update(i.e., correct) the prediction model.

The R2R controller 616 uses the assigned weights to generate aprocessing time, t_(i+1), to be used in the next wafer run. Controller616 is operative to dynamically adjust the weights assigned to theactual and virtual metrology parameters for each run as a function ofprediction and metrology error. In this manner, the R2R controller 616is beneficially able to optimize the sampling policy (e.g., minimizingsampling frequency) while maintaining a desired level of wafer qualityor alternative process metric.

Consider an illustrative scenario in which y_(i) is the depositionthickness of the i^(th) wafer, r _(i) is the average deposition rate ofthe i^(th) wafer, and t_(i) is the deposition time of the wafer. In afirst example representing R2R control in which actual and virtualmetrology parameters are not used in combination, the deposition time,t_(i+1), of the next wafer is determined as:

t i + 1 = Twhere T is a target of y_(i). In a second example utilizing both actualand virtual metrology results, the deposition time, t_(i+1), of the nextwafer is determined as:

${t_{i + 1} = \frac{T}{{\alpha\;{\overset{\_}{r}}_{i,{- 1}}} + {( {1 - \alpha} )}}},{0 \leq \alpha \leq 1}$where α is an assigned weight. In a third example, factors other thanactual and virtual metrology parameters, such as, but not limited to,uncertainty and chamber capabilities (e.g., chamber matching), areincorporated into the calculation of the deposition time, t_(i+1), ofthe next wafer as follows:

${t_{i + 1} = \frac{T}{{{\alpha(ɛ)}{\overset{\_}{r}}_{j,{- 1}}} + {\lbrack {1 - {\alpha(ɛ)}} \rbrack}}},{0 \leq {\alpha(ɛ)} \leq 1},{j \leq i}$where α(ε) in this instance can be expressed as metrology variation

${\alpha(ɛ)} = \frac{{var}{()}}{{{var}( y_{j} )} + {{var}{()}}}$or${{\alpha(ɛ)} = ( \frac{ɛ_{- 1}^{T}}{\max( {ɛ_{- m}^{T}} )} )^{2}},$where |ε⁻¹ ^(T)| is a prediction error corresponding to the last actualmetrology and max(|ε_(−m) ^(T)|) is a maximum absolute prediction erroramong the last m wafers.

FIG. 7 is a flow diagram depicting at least a portion of an exemplarysampling policy optimization methodology 700, according to an embodimentof the invention. The sampling policy optimization methodology 700 maybe performed, for example, in the sampling optimization module 406 shownin FIG. 4. As apparent from FIG. 7, sampling policy optimizationmethodology 700 may utilize a plurality of factors, including, but notlimited to, a process target T 702, a metrology error (ME) 704, anactual metrology (AM) 706, process bias and variation results 708,virtual metrology (VM) 710 and a prediction error (PE) 712. In thisexample, the sampling policy to be optimized is sampling frequencyoptimization 716, although the invention is not limited to optimizationof sampling frequency.

One or more factors may influence one or more other factors. Forexample, actual metrology results 706 are used to estimate the metrologyerror 704 and/or process bias and variation factor 708. Likewise, agiven factor may be a function of more than one other factor. Forexample, process bias and variation, in this illustration, can beestimated based on both actual metrology 706 and virtual metrology 710.Actual metrology 706 and metrology error 704 are used to estimate andcontrol metrology tool matching 714. An output indicative of metrologytool matching 714 is provided to the sampling frequency optimization716.

By way of example only and without loss of generality, consider a logicfunction to trigger different policies, ƒ(ME,ME*,C_(pk),C*,PE*,PE,T,AM,VM). A first exemplary policy may be expressed as

${{SF} = \frac{{SF}^{*}}{{\beta_{1}( C_{pk} )} + {\beta_{2}({ME})}}},$where C_(pk) and C* represent the process capability and its minimumallowed values in normal production, respectively, β₁(C_(pk)) representsnormalized C_(pk) and β₂(ME) represents normalized metrology error. Asecond policy may be expressed as

${{SF} = {{SF}^{*} \cdot \frac{{var}({VM})}{{{var}({VM})} + {{var}({AM})}}}},$where SF* represents minimum sampling frequency, and var(VM) and var(AM)represent the variance of the virtual metrology and actual metrology,respectively.

Assume an objective of the policy is to keep the measurement frequencyat a minimum (SF*), for example, one out of eight lots and six wafersper sampled lot, when the following conditions are met:

-   -   metrology error (ME) is less than or equal to a prescribed        minimum ME (ME≦ME*), C_(pk)≧C*, and prediction error (PE) is        less than or equal to a prescribed minimum PE (PE≦PE*);    -   actual metrology (AM) and virtual metrology (VM) are in-control        (SPC); and    -   metrology tool matching is within a prescribed tolerance.        Otherwise, if the above conditions are not met, increase the        sampling frequency to SF. For example, when metrology tool        mismatch indicates high measurement variation/bias, more        measurements need to be collected to compensate for the error.

A desired value, SF, for the sampling frequency can be determined from adynamic function of factors, like tool matching parameters, variance ofVM, metrology errors, etc., as described above. In one embodiment, amethod for determining SF includes steps of:

-   -   After processing a given wafer, retrieve the processing        variables and assess the following criteria:        -   PE≦PE*        -   Workload of the metrology tools        -   C_(pk) based on the actual and virtual metrology≧C_(pk)*        -   Baseline measurement frequency established based on sampling            frequency optimization    -   If any criterion is violated, measure the wafer; else, compute a        weighted criterion, C    -   If C>C*, measure the wafer; else, continue

With reference now to FIG. 8, a flow diagram conceptually depicts atleast a portion of an exemplary methodology 800 for generating ametrology-based prediction model, according to an embodiment of theinvention. The methodology 800 is operative to receive variousinformation, such as distance to the last measured wafer 802, which isindicative of the time since the last actual metrology was performed,and other factors 804 relating to the processing. The variousinformation received may be referred to herein as predictors, since theyare used in generating the metrology-based prediction model.

According to method 800, these received predictors are decomposed 806into at least two types: namely, a first type (Type I) comprisingvariance profiles (e.g., the variance curve of deposition thickness overthe number of wafers since the last measurement), and a second type(Type II). Weight components for Type I predictors 808 arepre-computable (e.g., based on equation (4A) and variance profilecurves) and retrieved from a knowledge base (e.g., database) oralternative storage element. Type II predictors 810 are obtained basedon dynamic regression models (e.g., equations (5) or (6)). Weightcomponents for type II predictors are obtained based onregression-driven predictor variance estimates. At least a subset of thetype I predictors 808 and at least a subset of the type II predictors810 are combined 814 to generate, as an output of method 800, a combinedpredictor 816. Different weights indicative of a statistical confidencein the respective predictor types can be assigned to the type I and typeII predictors (based on respective weight components), as previouslydescribed.

One or more embodiments of the invention, or elements thereof, can beimplemented in the form of an apparatus including a memory and at leastone processor that is coupled to the memory and operative to performexemplary method steps.

In accordance with various embodiments, the methods, functions, and/orlogic described herein are implemented as one or more software programsrunning on a computer processor. Dedicated hardware implementationsincluding, but not limited to, application specific integrated circuits,programmable logic arrays and other hardware devices are configured toimplement the methods described herein. Further, alternative softwareimplementations including, but not limited to, distributed processing orcomponent/object distributed processing, parallel processing, or virtualmachine processing are configured to implement the methods, functions,or logic described herein.

The embodiment contemplates a machine-readable medium orcomputer-readable medium containing instructions, or that which receivesand executes instructions from a propagated signal so that a deviceconnected to a network can send or receive voice, video or data, and tocommunicate over the network using the instructions. The instructionsmay be further transmitted or received over a network via a networkinterface device(s). The machine-readable medium also contains a datastructure for storing data useful in providing a functional relationshipbetween the data and a machine or computer in an illustrative embodimentof the systems and methods herein.

While the machine-readable medium may be embodied in a single medium,the term “machine-readable medium” should be taken to include a singlemedium or multiple media (e.g., a centralized or distributed database,and/or associated caches and servers) that store the one or more sets ofinstructions. The term “machine-readable medium” shall also be taken toinclude any medium that is capable of storing, encoding, or carrying aset of instructions for execution by the machine and that cause themachine to perform anyone or more of the methodologies of theembodiment. The term “machine-readable medium” shall accordingly betaken to include, but not be limited to: solid-state memories such as amemory card or other package that houses one or more read-only(non-volatile) memories, random access memories, or other re-writable(volatile) memories; magneto-optical or optical medium such as a disk ortape; and/or a digital file attachment to e-mail or other self-containedinformation archive or set of archives is considered a distributionmedium equivalent to a tangible storage medium. Accordingly, theembodiment is considered to include anyone or more of a tangiblemachine-readable medium or a tangible distribution medium, as listedherein and including art-recognized equivalents and successor media, inwhich the software implementations herein are stored.

It should also be noted that software, which implements the methods,functions or logic herein, are optionally stored on a tangible storagemedium, such as: a magnetic medium, such as a disk or tape; amagneto-optical or optical medium, such as a disk; or a solid statemedium, such as a memory card or other package that houses one or moreread-only (non-volatile) memories, random access memories, or otherre-writable (volatile) memories. A digital file attachment to e-mail orother self-contained information archive or set of archives isconsidered a distribution medium equivalent to a tangible storagemedium. Accordingly, the disclosure is considered to include a tangiblestorage medium or distribution medium as listed herein and otherequivalents and successor media, in which the software implementationsherein are stored.

The illustrations of embodiments of the invention described herein areintended to provide a general understanding of the structure of thevarious embodiments, and they are not intended to serve as a completedescription of all the elements and features of apparatus and systemsthat might make use of the structures described herein. Many otherembodiments will become apparent to those of skill in the art uponreviewing the above description. Other embodiments are utilized andderived therefrom, such that structural and logical substitutions andchanges are made without departing from the scope of this disclosure.Figures are also merely representational and are not necessarily drawnto scale. Certain proportions thereof may be exaggerated, while othersdiminished in order to facilitate an explanation of the embodiments ofthe invention. Accordingly, the specification and drawings are to beregarded in an illustrative rather than a restrictive sense.

Such embodiments of the inventive subject matter are referred to herein,individually and/or collectively, by the term “embodiment” merely forconvenience and without intending to voluntarily limit the scope of thisapplication to any single embodiment or inventive concept if more thanone is in fact shown. Thus, although specific embodiments have beenillustrated and described herein, it should be appreciated that anyarrangement calculated to achieve the same purpose are substituted forthe specific embodiments shown. This disclosure is intended to cover anyand all adaptations or variations of various embodiments. Combinationsof the above embodiments, and other embodiments not specificallydescribed herein, will be apparent to those of skill in the art uponreviewing the above description.

In the foregoing description of the embodiments, various features aregrouped together in a single embodiment for the purpose of streamliningthe disclosure. This method of disclosure is not to be interpreted asreflecting that the claimed embodiments have more features than areexpressly recited in each claim. Rather, as the following claimsreflect, inventive subject matter lies in less than all features of asingle embodiment. Thus the following claims are hereby incorporatedinto the Detailed Description, with each claim standing on its own as aseparate example embodiment.

The Abstract is provided to comply with 37 C.F.R. §1.72(b), whichrequires an abstract that will allow the reader to quickly ascertain thenature of the technical disclosure. It is submitted with theunderstanding that it will not be used to interpret or limit the scopeor meaning of the claims. In addition, in the foregoing DetailedDescription, it can be seen that various features are grouped togetherin a single embodiment for the purpose of streamlining the disclosure.This method of disclosure is not to be interpreted as reflecting anintention that the claimed embodiments require more features than areexpressly recited in each claim. Rather, as the following claimsreflect, inventive subject matter lies in less than all features of asingle embodiment. Thus the following claims are hereby incorporatedinto the Detailed Description, with each claim standing on its own asseparately claimed subject matter.

Although specific example embodiments have been described, it will beevident that various modifications and changes are made to theseembodiments without departing from the broader scope of the inventivesubject matter described herein. Accordingly, the specification anddrawings are to be regarded in an illustrative rather than a restrictivesense. The accompanying drawings that form a part hereof, show by way ofillustration, and without limitation, specific embodiments in which thesubject matter are practiced. The embodiments illustrated are describedin sufficient detail to enable those skilled in the art to practice theteachings herein. Other embodiments are utilized and derived therefrom,such that structural and logical substitutions and changes are madewithout departing from the scope of this disclosure. This DetailedDescription, therefore, is not to be taken in a limiting sense, and thescope of various embodiments is defined only by the appended claims,along with the full range of equivalents to which such claims areentitled.

Given the teachings of the invention provided herein, one of ordinaryskill in the art will be able to contemplate other implementations andapplications of the techniques of the invention. Although illustrativeembodiments of the invention have been described herein with referenceto the accompanying drawings, it is to be understood that the inventionis not limited to those precise embodiments, and that various otherchanges and modifications are made therein by one skilled in the artwithout departing from the scope of the appended claims.

What is claimed is:
 1. An apparatus for performing run-to-run controland sampling optimization in a semiconductor manufacturing process, theapparatus comprising: at least one control module operative: todetermine a process output and corresponding metrology error associatedwith an actual metrology for a current processing run in thesemiconductor manufacturing process; to determine a predicted processoutput and corresponding prediction error associated with a virtualmetrology for the current processing run; to control at least oneparameter corresponding to a subsequent processing run as a function ofthe metrology error and the prediction error; to obtain a predictionmodel associated with the semiconductor manufacturing process, theprediction model being adapted to predict the process output byestimating at least one processing parameter for the semiconductormanufacturing process; and to perform virtual metrology based on theprediction model, the prediction error being determined as a function ofan output of the virtual metrology; wherein the prediction modelcomprises a wafer quality prediction model for metrology variableprediction which utilizes tensor input process variables by directlyoperating on the tensor input process variables.
 2. The apparatus ofclaim 1, wherein the at least one control module is further operative:to measure at least one target processing parameter corresponding to awafer fabricated in the current processing run; to compare the measuredat least one target processing parameter with an expected value for theat least one target processing parameter; and to determine the metrologyerror as a function of a variation between the measured at least onetarget processing parameter and the expected value for the at least onetarget processing parameter.
 3. The apparatus of claim 1, wherein theprediction model comprises at least one of a single processing chamberbased model, a global model across a plurality of processing chambers, ametrology-based prediction model, and a metrology and error-adaptivemodel.
 4. The apparatus of claim 3, wherein the global model isgenerated by approximating coefficients corresponding to differentprocessing chambers to a common vector given by prior information ontool capability matching, adding a positive coefficient to balancedifferent terms in the global model, and minimizing the prediction errorand optimizing the approximation.
 5. The apparatus of claim 4, whereinthe at least one control module is operative to use a block coordinatebased algorithm for optimizing the approximation.
 6. The apparatus ofclaim 3, wherein, in constructing the metrology-based prediction model,the at least one control module is operative: to obtain a plurality ofpredictors, the predictors comprising information relating to thesemiconductor manufacturing process; to decompose the predictors into atleast two types, a first type comprising variance profiles, and a secondtype obtained based on dynamic regression models; and to generate acombined predictor comprising at least a subset of the first type ofpredictors and at least a subset of the second type of predictors. 7.The apparatus of claim 1, wherein the at least one control module isfurther operative: to assign a first weight to the metrology error and asecond weight to the prediction error, the first and second weightsbeing indicative of a confidence in the metrology error and predictionerror, respectively; and to control the at least one parametercorresponding to a subsequent processing run as a function of the firstand second weights.
 8. The apparatus of claim 7, wherein the first andsecond weights are dynamically adjusted in accordance with a confidencein the metrology error and prediction error, respectively, over time. 9.The apparatus of claim 7, wherein each of the first and second weightsis a percentage, with a sum of the first and second weights being equalto one.
 10. The apparatus of claim 7, wherein the at least one controlmodule is further operative to optimize a sampling policy correspondingto the semiconductor manufacturing process as a function of the firstand second weights.
 11. The apparatus of claim 7, wherein respectivevalues of the first and second weights are determined as a function ofone or more factors related to uncertainty and chamber matchingcapabilities associated with the semiconductor manufacturing process.12. An apparatus for performing run-to-run control and samplingoptimization in a semiconductor manufacturing process, the apparatuscomprising: at least one control module operative: to determine aprocess output and corresponding metrology error associated with anactual metrology for a current processing run in the semiconductormanufacturing process; to determine a predicted process output andcorresponding prediction error associated with a virtual metrology forthe current processing run; to control at least one parametercorresponding to a subsequent processing run as a function of themetrology error and the prediction error; to assign a first weight tothe metrology error and a second weight to the prediction error, thefirst and second weights being indicative of a confidence in themetrology error and prediction error, respectively; to control the atleast one parameter corresponding to a subsequent processing run as afunction of the first and second weights; and to optimize a samplingpolicy corresponding to the semiconductor manufacturing process as afunction of the first and second weights; wherein the at least onecontrol module is further operative to optimize the sampling policy byminimizing a sampling frequency of the semiconductor manufacturingprocess, the sampling frequency being indicative of at least one of anumber of processing runs and a number of wafers between consecutivemetrology measurements obtained during actual metrology.
 13. Anapparatus for performing run-to-run control and sampling optimization ina semiconductor manufacturing process, the apparatus comprising: atleast one control module operative: to determine a process output andcorresponding metrology error associated with an actual metrology for acurrent processing run in the semiconductor manufacturing process; todetermine a predicted process output and corresponding prediction errorassociated with a virtual metrology for the current processing run; tocontrol at least one parameter corresponding to a subsequent processingrun as a function of the metrology error and the prediction error; toassign a first weight to the metrology error and a second weight to theprediction error, the first and second weights being indicative of aconfidence in the metrology error and prediction error, respectively; tocontrol the at least one parameter corresponding to a subsequentprocessing run as a function of the first and second weights; and tooptimize a sampling policy corresponding to the semiconductormanufacturing process as a function of the first and second weights;wherein the at least one control module is further operative to optimizethe sampling policy by maximizing a time between actual metrologymeasurements obtained in connection with the semiconductor manufacturingprocess.
 14. An apparatus for performing run-to-run control and samplingoptimization in a semiconductor manufacturing process, the apparatuscomprising: at least one control module operative: to determine aprocess output and corresponding metrology error associated with anactual metrology for a current processing run in the semiconductormanufacturing process; to determine a predicted process output andcorresponding prediction error associated with a virtual metrology forthe current processing run; to control at least one parametercorresponding to a subsequent processing run as a function of themetrology error and the prediction error; to assign a first weight tothe metrology error and a second weight to the prediction error, thefirst and second weights being indicative of a confidence in themetrology error and prediction error, respectively; and to control theat least one parameter corresponding to a subsequent processing run as afunction of the first and second weights; wherein the at least onecontrol module is further operative to calculate a given one of thefirst and second weights according to an expression${{\alpha(ɛ)} = \lbrack \frac{ɛ_{- 1}^{T}}{\max( {ɛ_{- m}^{T}} )} \rbrack^{2}},$ where α(ε) represents the given one of the first and second weights,ε⁻¹ ^(T) represents a prediction error corresponding to a most recentactual metrology, and max (|ε_(−m) ^(T)|)represents maximum absoluteprediction error among the last m wafers, m being an integer.
 15. Acomputer program product for performing run-to-run control and samplingoptimization in a semiconductor manufacturing process, said computerprogram product comprising a computer readable storage medium havingcomputer readable program code embodied therewith, said computerreadable program code comprising: computer readable program codeconfigured to determine a process output and corresponding metrologyerror associated with an actual metrology for a current processing runin the semiconductor manufacturing process; computer readable programcode configured to determine a predicted process output andcorresponding prediction error associated with a virtual metrology forthe current processing run; computer readable program code configured tocontrol at least one parameter corresponding to a subsequent processingrun as a function of the metrology error and the prediction error;computer readable program code configured to obtain a prediction modelassociated with the semiconductor manufacturing process, the predictionmodel being adapted to predict the process output by estimating at leastone processing parameter for the semiconductor manufacturing process;and computer readable program code configured to perform virtualmetrology based on the prediction model, the prediction error beingdetermined as a function of an output of the virtual metrology; whereinthe prediction model comprises a wafer quality prediction model formetrology variable prediction which utilizes tensor input processvariables by directly operating on the tensor input process variables.